First we assume that this is equal to zero
so what we notice is this is a sum of 2 perfect cube
recall that
a^3+b^3=(a+b)(a^2-ab+b^2)
125x^3+343=
(5x)³+(7)³=(5x+7)(25x²-35x+49)
now solve the part in second parenthasees because we can see that the first parenthasees (5x+7) is going to have a real root
remember quadratic formula
for ax^2+bx+c=0
x=
a=25
b=-35
c=49
x=
x=
x=
x=
x=
x=
x=
the comlex roots are
x=
and 
so what we notice is this is a sum of 2 perfect cube
recall that
a^3+b^3=(a+b)(a^2-ab+b^2)
125x^3+343=
(5x)³+(7)³=(5x+7)(25x²-35x+49)
now solve the part in second parenthasees because we can see that the first parenthasees (5x+7) is going to have a real root
remember quadratic formula
for ax^2+bx+c=0
x=
a=25
b=-35
c=49
x=
x=
x=
x=
x=
x=
x=
the comlex roots are
x=